Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.
Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.
We have $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z=(2 x)^{2}+(-y)^{2}+(z)^{2}+2(2 x)(-y)$$+2(-y)(z)+2(2 x)(z)$
$=[2 x+(-y)+z]^{2}$ (Using Identity $V$)
$=(2 x-y+z)^{2}=(2 x-y+z)(2 x-y+z)$
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